I was thinking whether you can connect keyboard, mouse, monitor to Pi, then connect Pi to your "real" computer via network somehow, to "use" your real computer as if it were next to you. That means, you see your real screen content at the Pi, move the mouse cursor via your mouse at the Pi, can start real applications there, etc. Would this maybe be possible?

There's a program called Synergy that will let me use the keyboard and mouse from one computer for the other (thinking about doing that for my Pi until I can get a real keyboard). However, you can't use the same monitor. Maybe someone who's good with C++ can modify it to use the monitor. Maybe?